Which expression is equivalent to $$ \sqrt{3} $$ ? $$ 3^{\frac{1}{2}} 3^{\frac{1}{3}} $$ $$ 3^{2} $$

Question

UpStudy AI · Accepted Answer

To determine which expression is equivalent to $$ \sqrt{3} $$, let's analyze each option:

1. $$ 3^{\frac{1}{2}} $$ is the correct expression for $$ \sqrt{3} $$ because it represents the square root of 3.

2. $$ 3^{\frac{1}{2}} 3^{\frac{1}{3}} $$ is not equivalent to $$ \sqrt{3} $$. When you multiply powers with the same base, you add the exponents. So, this expression is equivalent to $$ 3^{\frac{1}{2} + \frac{1}{3}} $$, which simplifies to $$ 3^{\frac{3}{6} + \frac{2}{6}} = 3^{\frac{5}{6}} $$. This is not the same as $$ \sqrt{3} $$.

3. $$ 3^{2} $$ is not equivalent to $$ \sqrt{3} $$. This expression represents 3 squared, which is 9.

Therefore, the expression that is equivalent to $$ \sqrt{3} $$ is $$ 3^{\frac{1}{2}} $$.
The expression equivalent to $$ \sqrt{3} $$ is $$ 3^{\frac{1}{2}} $$.

Which expression is equivalent to ?

Upstudy AI Solution

Answer

Solution

Bonus Knowledge

Related Questions

Latest Algebra Questions